There is a cube in which one pair of opposite faces is painted red ; the second pair of opposite faces is painted blue and the third pair of opposite faces is painted green. This cube is now cut into 216 smaller but identical cubes .
how many cues are there with ONLY green and ONLY blue faces bainted
Answers
Answer:
For any cube,
let x denote number of cuts.Then
No: of cubes with 3 faces colored = 8
No: of cubes with 2 faces colored = 12* (x-2) where 12 is the number of edges
No: of cubes with 1 faces colored = 6* (x-2)^2 where 6 is the number of faces
No: of cubes with 0 faces colored = (x-2)^3
Total cubes= x^3
Total inner cubes =(x-2)^2
Comming to the question..........
given 512 smaller cubes.so number of cuts=x=8 {cuberoot of 512)
Q1. No red = Total cubes - Cubes with red color
According to formula all colors are present on 8 cubes.
Now cubes with 2 colors = 12(x-2)... But here only 2 sides have red ,so number of satisfying edges is 4 out of 12.
hence eq. becomes 8(x-2)=8(8-2)=48
Now 1 face = 6(x-2)^2
here only 2 faces in red
So eq. becomes 2(x-2)^2=72
Adding all three , we get 8+48+72=128..
So without red =512-128=384
5 years agoHelpfull: Yes(22) No(2)
Answer:
Number of cubes with only green and only blue painted = 4 * 16 = 64 cubes.
Explanation:
What is Verbal reasoning ?
Verbal reasoning is the comprehension and reasoning of ideas expressed in language. Instead of focusing just on fluency or word knowledge, it seeks to assess the student's capacity for critical thought.
Questions on this subject often include painting a cube with side measurements of "x" on each face and then cutting it into smaller cubes with side measurements of "y." The next step is to determine how many cubes have "n" painted faces.
The number of smaller cubes is the first thing you need to determine. You do this by counting the number of tiny cubes that can fit inside a specific edge of the large cube. It'll be x or y. Consequently, (x/y)3 smaller cubes will be present.
Painting a cube with side measurements of "x" on each face of the cube and then cutting it into smaller cubes with side measurements of "y" are common examples of questions on this topic. The number of cubes with "n" painted on their faces must be determined next.
The first thing you need to decide is how many smaller cubes there will be. You may determine this by counting how many little cubes can fit inside a certain edge of the big cube. X or Y will happen. As a result, there will be (x/y)3 smaller cubes.
If the length of the samller cubes that are cut is 1 unit.
Volume of each cube is 1 cu. units.
Volume of the bigger Cube 216 *1 = 216 cu. units
Length of each edge of the bigger cude = units
There will be 6*6 = 36 cubes in each face.
Now,
The cubes at the edges will have 2 different colours.
Number of cubes with only one colour in one face = 36 -(6 * 4 - 4) = 16 small cubes.
Number of cubes with only green and only blue painted = 4 * 16 = 64 cubes.
To learn more about verbal Reasoning refer to :
https://brainly.in/question/8722333?referrer=searchResults
https://brainly.in/question/8374753?referrer=searchResults
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